Chapter 20 - Magnetic Forces and Fields
• Magnets can exert forces on each other - like poles repel, unlike poles attract.
• The magnetic force acts through the magnetic field. See examples of the
magnetic field of a bar magnet.
• Magnetic fields exert forces on a charged particle.
• If the charge is stationary, the magentic field exerts no force.
• The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field.
• The magnetic field runs from N to S. poles.
• The definition of the magnetic field comes from the force that is exerted on
a charged particle in a magnetic field
B=
F
,
|q0 |(vsinθ)
where F is the magnitude of the force on the test charge, |q0 | is the magnitude of the test charge and v is the magnitude of the charge’s velocity and
θ is the angle between the direction of the magnetic field and the charge’s
velocity.
• The unit of the magnetic field is the Tesla, and 1 gauss = 10−4 tesla.
• The Right Hand rule no 1 gives the direction of the force - see figure 21.8,
p. 640. This is the direction of the magnetic force on a positively charged
particle. A negatively charged particle will have a magnetic force in the
opposite direction.
• Cross and dot notation to indicate fields going into and out of the paper.
• A charged particle executes a circular pathe while moving in a magnetic
field. The magnetic force always remains perpendicular to the velocity and
is directed toward the center of the circular path. The radius of this circular
path is
mv
.
r=
|q|B
• Ex 3, p. 644.
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• Force on a Current in a Magnetic Field is
F = ILBsinθ,
where I is the current, L is the length of the wire, and B is the magnetic
field. See example 5, p. 648.
• The torque on a current carrying wire. When a current carrying loop is
placed in a magnetic field, the loop tends to rotate such that its normal
becomes aligned with the magnetic field - example 6, p. 650.
• For N loops this is
τ = NIA(Bsinφ),
where I is the current, A is the area of the loop, B is the magnetic field
and φ is the angle the field makes to the loop normal.
• This is how an electriic motor works. Opposite to a generator.
• Electrical Currents produce magnetic fields.
• Second Right Hand rule - p. 651.ves the direction of the magnetic field
around an infinitley long straight wire.
• The magnitude of such a field is given by
B=
µ0 I
,
2πr
where µ0 is the magnetic permeability of free space and µ0 = 4π×10−7 T.m/A.
• Example 7, p. 652, Example 8, p. 652.
• Magnetic field at the center of N loops of wire,
B=N
µ0 I
,
2R
where I is the current and R is the radius of the loop.
• The direction of the magnetic field here is given by the Right Hand rule,
figure 21.29, p. 656.
• Example 10, p. 656.
• A solenoid is n loops of wire - it has magnetic field B = µ0 nI.
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